Question

find 10 rational number between 1/2 and 2/3.

Answer 1

Take Lcm of 2 & 3 it is 6
Then the two numbers will be 3/6 & 4/6we have to find out 10 rational numbers means just take one number above it is 11.

Multiply and divide both 3/6 & 4/6 by 11 we get
33/66 & 44/66
Therefore the rational numbers between them are
34/66, 35/66, 36/66, 37/66, 38/66, 39/66, 40/66, 41/66, 42/66, 43/66
Just reduce the fractions if it can be done
17/33, 35/66, 6/11, 37/66, 19/11, 13/22, 20/33, 41/66, 7/11 & 43/66

Answer 2

To find:

10 rational numbers between $\frac{1}{2}$ and $\frac{2}{3}$.

Solution:

Take LCM and make the denominators equal.

LCM of 2 and 3 = 6

$\frac{1}{2}\times \frac{3}{3} =\frac{3}{6}$

$\frac{2}{3}\times \frac{2}{2} =\frac{4}{6}$

Multiply and divide both fractions by 11.

$\frac{3}{6}\times \frac{11}{11} =\frac{33}{66}$

$\frac{4}{6}\times \frac{11}{11} =\frac{44}{66}$

10 rational numbers are:

$\frac{34}{66} , \ \frac{35}{66}, \ \frac{36}{66}, \ \frac{37}{66}, \ \frac{38}{66}, \ \frac{39}{66}, \ \frac{40}{66}, \ \frac{41}{66}, \ \frac{42}{66}, \ \frac{43}{66}$

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